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Geodesic languages for rational subsets and conjugates in virtually free groups
André Carvalho, Pedro V. Silva
We prove that a subset of a virtually free group is rational if and only if the language of geodesic words representing its elements (in any generating set) is rational and that th…
On supratopologies, normalized families and Frankl conjecture
André Carvalho, António Machiavelo
We introduce some generalized topological concepts to deal with union-closed families, and show that one can reduce the proof of Frankl's conjecture to some families of so-called s…
Free-abelian by free groups: homomorphisms and algorithmic explorations
André Carvalho, Jordi Delgado
We obtain an explicit description of the endomorphisms of free-abelian by free groups together with a characterization of when they are injective and surjective. As a consequence w…
Orbit problems for free-abelian times free groups and related families
André Carvalho, Jordi Delgado
We prove that the Brinkmann Problems (BrP & BrCP) and the twisted-conjugacy Problem (TCP) are decidable for any endomorphism of a free-abelian times free (FATF) group Fn x Z^m. Fur…